Without the sequences and commands used to erase and install here, I'm left to guess as to what happened here. I don't know which Mac is involved here, either — some of these have internet recovery and which can sometimes be useful here, and some do not.
If the whole disk was erased and reformatted, there should be nothing on the system — beyond the pieces and parts associated with the file system structures — that was not then installed.
In general, boot from a locally-created USB boot disk, preferably created on a separate system, and using a new-to-you or new-to-the-target-system (ad disposable) USB device. Boot and use that to access the problematic disk.
If you want to know where you are currently defaulted to within the file system, use the pwd command.
Use the cd command to change the default.
EfiLoginUI is part of OS X.
Finding a .DS_Store file in various directories is expected, after a user of Finder has visited the directory.
The . and .. files (directories) are normal.
If the current default directory is /, then the ./Library path is not recursive.
With the ls command, the -a switch shows leading-dot "hidden" files, if the current user is not root or not sudo — where it's the default on ls.
The /etc/mach_init.d and /etc/mach_init_per_user.d directories are associated with some long-deprecated startup customization processing. That'd be worth a look, and compare that with what's present on a known-good system. (But again, a complete disk erasure — not a partition-level erasure — should remove all directories and all files on the target disk. You'll need that USB boot disk mentioned above, here.)
Get somebody to look at this box. Trying to do any sort of forensics via forum postings is far more time and effort. I'd probably image the whole disk somewhere to start; to create a complete copy of the whole disk. Then get somebody to look at it, as well as at at the USB device that reportedly was involved here. Or if you want to pursue this investigation yourself, there is an OS X internals book and at least one book on file system forensics does include some OS X file system info, and you can start reading. If you are unfamiliar with the general topic, Apple has a shell scripting primer available, too.